**Article:** Tirunagari, RR; Pope, SB; *“LES/PDF for Premixed Combustion in the DNS Limit”,* Combustion Theory and Modelling, 20(**5**):834-865

**Abstract: **We investigated the behaviour of the composition probability density function (PDF) model equations used in a large-eddy simulation (LES) of turbulent combustion in the direct numerical simulation (DNS) limit; that is, in the limit of the LES resolution length scale (and the numerical mesh spacing h) being small compared to the smallest flow length scale, so that the resolution is sufficient to perform a DNS. The correct behaviour of a PDF model in the DNS limit is that the resolved composition fields satisfy the DNS equations, and there are no residual fluctuations (i.e. the PDF is everywhere a delta function). In the DNS limit, the treatment of molecular diffusion in the PDF equations is crucial, and both the random-walk’ and mean-drift’ models for molecular diffusion are investigated. Two test cases are considered, both of premixed laminar flames (of thickness (L)). We examine the solutions of the model PDF equations for these test cases as functions of /(L) and h/(L). Each of the two PDF models has advantages and disadvantages. The mean-drift model behaves correctly in the DNS limit, but it is more difficult to implement and computationally more expensive. The random-walk model does not have the correct behaviour in the DNS limit in that it produces non-zero residual fluctuations. However, if the specified mixing rate normalised by the reaction timescale (c) is sufficiently large ((c) 1), then the residual fluctuations are less than 10% and the observed flame speed and thickness are close to their laminar values. Away from the DNS limit (i.e. h/(L) 1), the observed flame thickness scales with the mesh spacing h, and the flame speed scales with h. For this case it is possible to construct a non-general specification of the mixing rate such that the flame speed matches the laminar flame speed.

Funding Acknowledgement: US Department of Energy Office of Science, Office of Basic Energy Sciences [DE-FG02-90ER14128]

Funding Text: This material is based upon work supported by the US Department of Energy Office of Science, Office of Basic Energy Sciences [Award Number DE-FG02-90ER14128].